Question

If the circumference of the biggest of the concentric circles in the given image is 88V2 cm, what is the
22
area of the portion of the square that is shaded red (in cm)? (Take 7 =
7​

Answer 1

Answer:

Given,

2πr=374cm

2πR=396cm

Therefore,

2πr=374cm

=>r=

2×22

374×7

=59.5

2πR=396cm

=>R=

2×22

396×7

=63

Area of shaded portion=(πR

2

−πr

2

)cm

2

=π[(63)

2

−(59.5)

2

]cm

2

=π(3969−3540.25)

=1347.5cm

2

Answer 2

Answer:

The area of red portion of the square  is 168.2 cm²

Step-by-step explanation:

Step 1 of 2:

• Circumference of the circle shaded with black is $88\sqrt{2}$

     $2\pi r=88\sqrt{2}\\r=19.8 cm$

• Diameter of the circle is 2r

     $2*19.8\\=39.6 cm$

Step 2 of 2:

• For the given question,The diameter of the circle becomes diagonal of the square.
• let the side of the square is a.
• By Pythagoras theorem

         $a^{2} +a^{2} =d^{2} \\2a^{2} =39.61^{2} \\a=28 cm$

• Now, the side of square becomes the diameter of the Small circle of yellow color.
• The radius of circle is $\frac{28}{2} =14$
• Area of shaded region = area of square - area of circle

        $=a^{2} -\pi r^{2} \\=28^{2}-\pi 14^{2} \\=784-615.75\\=168.2 cm^{2}$